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用于因果推断与模型发现的连续时间集合 Kalman–Bucy 平滑器AI 解读

Data assimilation (DA) integrates observational information with model predictions to improve state estimation in complex systems. While filtering provides the basis for online forecasts by using only past and present observations, it can exhibit delays and biases when the underlying dynamics evolve rapidly or undergo regime transitions. Smoothing, which additionally incorporates future observations, provides a natural pipeline for hindcasting and reanalysis that yields an…

变量投影稀疏函数主成分分析：可解释降维及拉曼光谱应用AI 解读

Functional principal component analysis (FPCA) provides low-rank representations of functional data but generally produces dense components, making it difficult to identify the localised regions contributing to dominant modes of variation. This limitation is particularly relevant in Raman spectroscopy, where spectra are observed over an ordered domain and interpretation often focuses on chemically meaningful spectral regions. This study proposes variable-projection sparse…

下尾Spearman相关曲线的Bernstein平滑估计与自助推断AI 解读

This paper studies a Bernstein-smoothed plug-in estimator for the lower-tail Spearman's rho curve, a rank-based measure of local concordance defined through a normalized copula integral over the lower-left square $[0,p]^2$. The estimator applies the lower-tail Spearman functional to the empirical Bernstein copula and introduces a degree parameter that controls finite-sample regularization. The contribution is target-specific estimation and inference for the lower-tail…

因果推断中双重稳健双重／去偏机器学习估计的协变量选择AI 解读

High-dimensional data create challenges for causal effect estimation because identifying the covariates needed for correct model specification becomes increasingly difficult. Double/debiased machine learning (DML) facilitates the use of machine learning (ML) for causal inference by mitigating regularization and overfitting bias, but comparatively less attention has been given to covariate selection in relation to the double robustness (DR) property possessed by some DML…

风险比较定理及其在扩散系数深度学习中的应用AI 解读

We investigate the nonparametric estimation of the diffusion matrix in stochastic differential equations featuring multidimensional, strong mixing covariate processes. We propose a flexible statistical framework based on general function classes that does not require a linear basis representation, rendering our results directly applicable to deep neural network estimators. Our approach employs a two-step estimation procedure: constructing a preliminary nonparametric…

核心—边缘网络的惩罚最大似然推断AI 解读

Likelihood-based network models are often fitted under links' independence and low-order constraints, while empirical networks frequently exhibit systematic higher-order structures such as triangles and wedges, characterizing the observed clustering patterns. Real-world core-periphery networks such as the interbank market or the air transportation system represent key examples, with cores displaying complex and nonlinear features. We formalize Penalized Likelihood with…

高维非平稳时间序列中多个同时变点的检测AI 解读

This paper studies the detection of multiple simultaneous (systematic) change points for high-dimensional nonstantionary economic and financial time series data. The analytic framework used is based on the standard and adaptive fused group lasso method, where the mixed L_{2,1} penalty is either uniform or re-weighted by data-dependent weights. This paper shows that, under appropriate conditions, this approach is L_2 consistent and, by adopting the data-dependent weights,…

基于统计微分方案的抗噪声惩罚算子AI 解读

Classical approaches to penalized smoothing often rely on basis or kernel expansions, which constrain the estimator to a fixed span and may be restrictive for discretely observed data. We instead regularize a single noisy trajectory directly on its observation grid, using difference operators that remain genuine finite-difference approximations to derivatives while being statistically normalized and mutually decorrelated under a reference noise law. We extend this…

惩罚变换分布回归：兼顾可解释性与协变量依赖的形状灵活性AI 解读

A central challenge in distributional regression is to allow the shape of the conditional distribution of the response variable to vary flexibly with covariates while retaining directly interpretable effects on its mean and standard deviation. We extend the penalized transformation model (PTM) family into a conditional-shape PTM, which assigns separate structured additive predictors to the conditional mean, standard deviation, and standardized distributional shape beyond…

有限混合回归模型的分量加权稀疏组 LASSOAI 解读

When analyzing heterogeneous data with latent subpopulations, finite mixture regression (FMR) models are effective as they allow for variations in regression coefficients across mixture components. Variable selection is important at two levels: (1) at the group level by removing completely irrelevant covariates across all subpopulations and (2) at the individual level by removing irrelevant covariates within each subpopulation. However, existing variable selection methods…

分位数回归的分布式选择后推断AI 解读

We propose a distributed selective inference framework tailored for high-dimensional quantile regression. To enable valid post-selection inference in this context, we address the computational challenge posed by the non-smooth quantile loss via a response-surrogation strategy. This strategy transforms the problem into a penalized least-squares formulation, thereby facilitating distributed selective inference. For valid post-selection inference, a randomized procedure is…

设计信息辅助的回归AI 解读

We consider regression problems in which the marginal distribution of the covariates is informative for estimation and variable selection, rather than merely auxiliary. Motivated by random-design, high-dimensional, and latent-effect settings, we propose a general design-assisted regression framework in which the estimating criterion depends on both the conditional model for $Y \mid \bfX$ and structured features of the covariate distribution. The framework identifies two…

拟最大似然断点估计的锐信噪比阈值AI 解读

We establish a sharp pathwise signal-to-noise criterion for quasi-maximum-likelihood (QML) estimation of a dominant breakpoint in the second-moment structure of a multivariate time series: the QML estimator is consistent whenever the between-regime contrast exceeds the within-regime fluctuation by an explicit factor, and below this threshold global recovery can fail. Two innovations drive the result. First, the framework is pathwise: no stochastic model is imposed on the…

缺失数据下广义潜因子模型的初始化、隐式正则化与推断AI 解读

Generalized latent factor models provide a flexible framework for analyzing high-dimensional non-Gaussian data, but principled estimation and uncertainty quantification under missingness remain substantially less developed. We develop a theory that connects a computationally tractable nonconvex procedure directly to statistical inference for nonlinear latent factor models with exponential-family links and partially observed entries. Our procedure combines a link-aware…

熵正则化逆强化学习的统计分析AI 解读

Inverse reinforcement learning aims to infer the reward function that explains expert behavior observed through trajectories of state--action pairs. A long-standing difficulty in classical IRL is the non-uniqueness of the recovered reward: many reward functions can induce the same optimal policy, rendering the inverse problem ill-posed. In this paper, we develop a statistical framework for Inverse Entropy-regularized Reinforcement Learning that resolves this ambiguity by…

心理测量结局缺失时高维预测变量的贝叶斯选择AI 解读

High-dimensional, multimodal predictors and partially observed multivariate outcomes are common in psychometric research. However, existing regularization methods often do not accommodate hierarchical predictor structures and are primarily designed for univariate outcomes. We propose SHIM, a Bayesian framework for structured variable selection that combines hierarchical horseshoe shrinkage with a Bayesian treatment of missing outcomes. The framework jointly accommodates…

基于正交机器学习的非参数异质性因果中介分析AI 解读

Causal mediation analysis decomposes the total effect of an intervention on an outcome into a direct pathway and an indirect pathway transmitted through a mediator, but standard methods typically summarize these pathways using population average effects. In many applications, however, the indirect effect may vary substantially across individual profiles. We propose an orthogonal statistical learning framework for estimating heterogeneous causal mediation effects conditional…

稀疏正则化多边际最优传输与重心的中心极限定理及自助法AI 解读

Wasserstein barycenters are a fundamental tool for the analysis of distribution-valued data, but their computation and statistical analysis become challenging in high-dimensional and multi-sample settings. The unregularized barycenter problem is computationally demanding and suffers severely from the curse of dimensionality, making regularization essential in many applications. While regularized optimal transport methods are widely used, approaches based on entropic…

Lipschitz 谱算法下 RKHS 回归与序列模型的风险等价AI 解读

Kernel spectral algorithms are often summarized by convergence rates, which hide how their risk depends jointly on regularization, noise, the population spectrum, target coefficients, and the chosen filter. Gaussian sequence models arise as a simplified but characteristic setting for studying the interplay of these factors, where the kernel spectral algorithm corresponds to a coordinatewise shrinkage estimator. Under mild assumptions, we show that the risk of a kernel…

基于结构信息的迁移学习AI 解读

Transfer learning improves estimation in a target study using information from related sources. Classical transfer learning is typically data-based, requiring access to the source data or to a model fitted on them. Neither is available in many modern studies, as both are often proprietary or unreported. What can be transferred instead is structure: summarized information derived from a source, such as the supports of predictors, which is available and interpretable without…

集成信息滤波：在集成卡尔曼方法中学习与编码稀疏结构AI 解读

Ensemble-based Data Assimilation faces significant challenges in high-dimensional systems due to spurious correlations and ensemble collapse. We propose the Ensemble Information Filter, which addresses these issues by encoding locality directly in the precision matrix through sparse Markov structure. This approach is motivated by connections to SPDE-based models, where local operators induce sparse precision representations and provide a principled form of regularisation.…

具有结构化收缩与持续性先验的贝叶斯广义网络自回归模型AI 解读

We propose a Bayesian generalized network autoregressive (BGNAR) model for multivariate time series whose component series are associated with the nodes of a known network. The proposed framework combines the parsimonious network structure of the generalized network autoregressive (GNAR) model with structured shrinkage and persistence priors adapted from Bayesian vector autoregressive (BVAR) modeling. We adapt Minnesota-type shrinkage to both own-lag and network-lag…

通过Johnson–Lindenstrauss变换实现差分隐私Model-X KnockoffsAI 解读

We introduce a novel privatization framework for high-dimensional controlled variable selection. Our framework enables rigorous False Discovery Rate (FDR) control under differential privacy constraints. While the Model-X knockoff procedure provides FDR guarantees by constructing provably exchangeable ``negative control" features, existing privacy mechanisms like Gaussian noise injection disrupt its core exchangeability conditions. In this work we consider privatizing the…

收缩使 Hosmer–Lemeshow 检验失效：惩罚逻辑回归拟合优度及青光眼应用AI 解读

Clinical prediction models are increasingly fitted by penalized logistic regression, because collinearity or many candidate predictors makes maximum likelihood unstable or impossible. Calibration is then almost always assessed by a grouped goodness-of-fit test such as the Hosmer-Lemeshow test. We show that this combination is invalid. Under ridge regression the grouped standardized residuals acquire a non-centrality induced by shrinkage, so the reference distribution used in…